I would continue to the flare and go around then if I hadn't had a landing clearance.
If I'd got to flare position, I'd land and clear runway as quickly as possible. Going around would just occupy runway space for longer - and give a problem for a faster aircraft going around because of your unexpected appearance.
I've had one radio failure in the circuit at night. I discovered it when I was unable to get a response to my Final calls. I landed, and cleared runway, making blind transmissions, and phoned the tower.
You should have the ATC number on your phone - you'll have difficulty hearing them with engine noise unless you have an earphone, but they'll hear you.
As a student, the most important thing is to fly your aircraft, and not worry about inconviencing others - don't lose control while trying to phone, or crash trying to land somewhere else. I'd go to a farm strip and phone if I had an enroute radio failure, and my handheld also failed.
PS Check radio volume: Check headset volume:Check radio frequency - you can accidentaly flip the channel: Check headset plugs fully in: try other side sockets, using other ptt. If there's another headset, try it (If fitted, check anunciator panel switches.)